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Convergence of Fourier Series01:21

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The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
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WEDM: Wavelet-Enhanced Diffusion with Multi-Stage Frequency Learning for Underwater Image Enhancement.

Junhao Chen1, Sichao Ye2, Xiong Ouyang3

  • 1Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, China.

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|April 25, 2025
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Summary

This study introduces the Wavelet-based Enhancement Diffusion Model (WEDM) for underwater image enhancement. WEDM improves color and detail restoration by integrating wavelet transforms with diffusion models, addressing challenges in marine exploration.

Keywords:
diffusion modelsfrequency-domain processingunderwater image enhancementwavelet transform

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Area of Science:

  • Computer Vision
  • Image Processing
  • Marine Science

Background:

  • Underwater images suffer degradation from light absorption and scattering, causing color distortion and loss of detail.
  • Existing spatial-domain methods often overlook crucial frequency-domain information for texture and edge restoration.

Purpose of the Study:

  • To propose a novel underwater image enhancement (UIE) framework, the Wavelet-based Enhancement Diffusion Model (WEDM).
  • To leverage frequency-domain analysis and diffusion models for improved UIE.
  • To enhance visual quality for marine exploration and ecological monitoring applications.

Main Methods:

  • The proposed WEDM framework integrates frequency-domain decomposition with diffusion models.
  • It features a Wavelet Color Compensation Module (WCCM) for LAB color correction using discrete wavelet transform.
  • A Wavelet Diffusion Module (WDM) employs wavelet-based operations, replacing convolutions to preserve multi-scale frequency features.

Main Results:

  • The WEDM framework effectively reduces noise amplification and high-frequency blurring by combining residual denoising diffusion with frequency-specific processing.
  • Ablation studies confirmed the critical contributions of both WCCM and WDM to enhanced color fidelity and texture details.
  • The framework provides a robust solution for underwater visual tasks.

Conclusions:

  • The Wavelet-based Enhancement Diffusion Model (WEDM) offers a significant advancement in underwater image enhancement.
  • Its integration of wavelet transforms and diffusion models effectively addresses degradation issues.
  • WEDM shows strong potential for applications in marine exploration and ecological monitoring.